Numerical Strategies for Solving Multiparameter Spectral Problems

被引：3

作者：

Amodio, Pierluigi ^{[1
]}

Settanni, Giuseppina ^{[1
]}

机构：

[1] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, Italy

来源：

NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS, PT II | 2020年 / 11974卷

关键词：

Multiparameter spectral problems; High order methods; Finite difference schemes;

D O I：

10.1007/978-3-030-40616-5_23

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We focus on the solution of multiparameter spectral problems, and in particular on some strategies to compute coarse approximations of selected eigenparameters depending on the number of oscillations of the associated eigenfunctions. Since the computation of the eigenparameters is crucial in codes for multiparameter problems based on finite differences, we herein present two strategies. The first one is an iterative algorithm computing solutions as limit of a set of decoupled problems (much easier to solve). The second one solves problems depending on a parameter sigma is an element of [0, 1], that give back the original problem only when sigma = 1. We compare the strategies by using well known test problems with two and three parameters.

引用

页码：298 / 305

页数：8

共 46 条

[31] A finite differences MATLAB code for the numerical solution of second order singular perturbation problems [J].

Amodio, Pierluigi ;

Settanni, Giuseppina .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (16) :3869-3879

[32] High Order Finite Difference Schemes for the Numerical Solution of Eigenvalue Problems for IVPs in ODEs [J].

Amodio, Pierluigi ;

Settanni, Giuseppina .

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, 2010, 1281 :202-205

[33] Global spectral analysis of multi-level time integration schemes: Numerical properties for error analysis [J].

Sengupta, Tapan K. ;

Sengupta, Aditi ;

Saurabh, Kumar .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 304 :41-57

[34] OPTIMIZED EXPLICIT RUNGE-KUTTA SCHEMES FOR THE SPECTRAL DIFFERENCE METHOD APPLIED TO WAVE PROPAGATION PROBLEMS [J].

Parsani, M. ;

Ketcheson, David I. ;

Deconinck, W. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2013, 35 (02) :A957-A986

[35] A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation [J].

Beshtokov, M. Kh .

VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2021, 31 (03) :384-408

[36] Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers [J].

Natesan, S ;

Jayakumar, J ;

Vigo-Aguiar, J .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 158 (01) :121-134

[37] A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems [J].

Wang, Zhicheng ;

Triantafyllou, Michael S. ;

Constantinides, Yiannis ;

Karniadakis, George Em .

COMPUTERS & FLUIDS, 2018, 172 :84-96

[38] High accuracy wave simulation - Revised derivation, numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic [J].

Tong, Ping ;

Yang, Dinghui ;

Hua, Biaolong .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2011, 48 (01) :56-70

[39] Explicit eighth order methods for the numerical integration of initial-value problems with periodic or oscillating solutions [J].

Simos, TE .

COMPUTER PHYSICS COMMUNICATIONS, 1999, 119 (01) :32-44

[40] CABARET scheme for the numerical solution of aeroacoustics problems: Generalization to linearized one-dimensional Euler equations [J].

Goloviznin, V. M. ;

Karabasov, S. A. ;

Kozubskaya, T. K. ;

Maksimov, N. V. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2009, 49 (12) :2168-2182

← 1 2 3 4 5 →